Low-Dimensional Partial Integro-differential Equations for High-Dimensional Asian Options

2014 ◽  
pp. 331-348
Author(s):  
Peter Hepperger
Keyword(s):  
Differential Equations ◽  
High Dimensional ◽  
Asian Options ◽  
Low Dimensional

scholarly journals hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations

2021 ◽  
Vol 47 (4) ◽  
pp. 1-34
Author(s):  
Peter Munch ◽  
Katharina Kormann ◽  
Martin Kronbichler
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
High Dimensional ◽  
Partial Differential ◽  
Dimensional Phase Space ◽  
Dimensional Finite Element ◽  
Low Dimensional ◽  
Matrix Free ◽  
Level Performance

This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper.deal are reported for high-dimensional advection problems and for the solution of the Vlasov–Poisson equation in up to six-dimensional phase space.

Adaptive Dimensionality-Reduction for Time-Stepping in Differential and Partial Differential Equations

2017 ◽  
Vol 10 (4) ◽  
pp. 872-894 ◽  
Author(s):  
Xing Fu ◽  
J. Nathan Kutz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensionality Reduction ◽  
Slow Manifold ◽  
High Dimensional ◽  
Dimensional System ◽  
Partial Differential ◽  
Optimal Basis ◽  
Time Stepping ◽  
Low Dimensional

AbstractA numerical time-stepping algorithm for differential or partial differential equations is proposed that adaptively modifies the dimensionality of the underlying modal basis expansion. Specifically, the method takes advantage of any underlying low-dimensional manifolds or subspaces in the system by using dimensionality-reduction techniques, such as the proper orthogonal decomposition, in order to adaptively represent the solution in the optimal basis modes. The method can provide significant computational savings for systems where low-dimensional manifolds are present since the reduction can lower the dimensionality of the underlying high-dimensional system by orders of magnitude. A comparison of the computational efficiency and error for this method are given showing the algorithm to be potentially of great value for high-dimensional dynamical systems simulations, especially where slow-manifold dynamics are known to arise. The method is envisioned to automatically take advantage of any potential computational saving associated with dimensionality-reduction, much as adaptive time-steppers automatically take advantage of large step sizes whenever possible.

scholarly journals Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals

2020 ◽  
Vol 10 (5) ◽  
pp. 1797 ◽  
Author(s):  
Mera Kartika Delimayanti ◽  
Bedy Purnama ◽  
Ngoc Giang Nguyen ◽  
Mohammad Reza Faisal ◽  
Kunti Robiatul Mahmudah ◽  
...  
Keyword(s):  
Machine Learning ◽  
Sleep Stage ◽  
Machine Learning Algorithms ◽  
High Dimensional ◽  
Sleep Stages ◽  
Eeg Signals ◽  
Stage Classification ◽  
Sleep Stage Classification ◽  
Low Dimensional

Manual classification of sleep stage is a time-consuming but necessary step in the diagnosis and treatment of sleep disorders, and its automation has been an area of active study. The previous works have shown that low dimensional fast Fourier transform (FFT) features and many machine learning algorithms have been applied. In this paper, we demonstrate utilization of features extracted from EEG signals via FFT to improve the performance of automated sleep stage classification through machine learning methods. Unlike previous works using FFT, we incorporated thousands of FFT features in order to classify the sleep stages into 2–6 classes. Using the expanded version of Sleep-EDF dataset with 61 recordings, our method outperformed other state-of-the art methods. This result indicates that high dimensional FFT features in combination with a simple feature selection is effective for the improvement of automated sleep stage classification.

scholarly journals A Nonlinear Maximum Correntropy Information Filter for High-Dimensional Neural Decoding

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 743
Author(s):  
Xi Liu ◽  
Shuhang Chen ◽  
Xiang Shen ◽  
Xiang Zhang ◽  
Yiwen Wang
Keyword(s):  
State Estimation ◽  
Measurement Model ◽  
High Dimensional ◽  
Neural Firing ◽  
The Neural Network ◽  
Information Filter ◽  
Critical Technology ◽  
Dimensional Measurements ◽  
Non Gaussian ◽  
Low Dimensional

Neural signal decoding is a critical technology in brain machine interface (BMI) to interpret movement intention from multi-neural activity collected from paralyzed patients. As a commonly-used decoding algorithm, the Kalman filter is often applied to derive the movement states from high-dimensional neural firing observation. However, its performance is limited and less effective for noisy nonlinear neural systems with high-dimensional measurements. In this paper, we propose a nonlinear maximum correntropy information filter, aiming at better state estimation in the filtering process for a noisy high-dimensional measurement system. We reconstruct the measurement model between the high-dimensional measurements and low-dimensional states using the neural network, and derive the state estimation using the correntropy criterion to cope with the non-Gaussian noise and eliminate large initial uncertainty. Moreover, analyses of convergence and robustness are given. The effectiveness of the proposed algorithm is evaluated by applying it on multiple segments of neural spiking data from two rats to interpret the movement states when the subjects perform a two-lever discrimination task. Our results demonstrate better and more robust state estimation performance when compared with other filters.

PSS Business Case Map: Supporting Idea Generation in PSS Design

2012 ◽  
Author(s):  
Fumiya Akasaka ◽  
Kazuki Fujita ◽  
Yoshiki Shimomura
Keyword(s):  
Idea Generation ◽  
Business Case ◽  
Literature Survey ◽  
The Self ◽  
High Dimensional ◽  
Self Organizing Map ◽  
Two Dimensional ◽  
Service Type ◽  
Business Cases ◽  
Low Dimensional

This paper proposes the PSS Business Case Map as a tool to support designers’ idea generation in PSS design. The map visualizes the similarities among PSS business cases in a two-dimensional diagram. To make the map, PSS business cases are first collected by conducting, for example, a literature survey. The collected business cases are then classified from multiple aspects that characterize each case such as its product type, service type, target customer, and so on. Based on the results of this classification, the similarities among the cases are calculated and visualized by using the Self-Organizing Map (SOM) technique. A SOM is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional) view from high-dimensional data. The visualization result is offered to designers in a form of a two-dimensional map, which is called the PSS Business Case Map. By using the map, designers can figure out the position of their current business and can acquire ideas for the servitization of their business.

Description of transient states of von Kármán vortex streets by low‐dimensional differential equations

1990 ◽  
Vol 2 (4) ◽  
pp. 479-481 ◽  
Author(s):  
F. Ohle ◽  
P. Lehmann ◽  
E. Roesch ◽  
H. Eckelmann ◽  
A. Hübler
Keyword(s):  
Differential Equations ◽  
Transient States ◽  
Von Karman ◽  
Vortex Streets ◽  
Karman Vortex ◽  
Low Dimensional ◽  
Von Kármán

CHAOS AND HYPERCHAOS IN A CLASS OF SIMPLE CELLULAR NEURAL NETWORKS MODELED BY O.D.E.

2006 ◽  
Vol 16 (09) ◽  
pp. 2729-2736 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Exponents ◽  
Cellular Neural Networks ◽  
New Class ◽  
Connection Matrices ◽  
Low Dimensional

This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer.

scholarly journals Perspectives of the high-dimensional dynamics of neural microcircuits from the point of view of low-dimensional readouts

Complexity ◽  
2003 ◽  
Vol 8 (4) ◽  
pp. 39-50 ◽  
Author(s):  
Stefan Häusler ◽  
Henry Markram ◽  
Wolfgang Maass
Keyword(s):  
Point Of View ◽  
High Dimensional ◽  
Low Dimensional

Improved interactive color visualization approach for hyperspectral images

2021 ◽  
pp. 147387162110481
Author(s):  
Haijun Yu ◽  
Shengyang Li
Keyword(s):  
Real Time ◽  
Hyperspectral Images ◽  
High Dimensional ◽  
Interactive Control ◽  
Output Image ◽  
Dr Method ◽  
The Rich ◽  
Low Dimensional ◽  
Color Visualization ◽  
Fusion Coefficient

Hyperspectral images (HSIs) have become increasingly prominent as they can maintain the subtle spectral differences of the imaged objects. Designing approaches and tools for analyzing HSIs presents a unique set of challenges due to their high-dimensional characteristics. An improved color visualization approach is proposed in this article to achieve communication between users and HSIs in the field of remote sensing. Under the real-time interactive control and color visualization, this approach can help users intuitively obtain the rich information hidden in original HSIs. Using the dimensionality reduction (DR) method based on band selection, high-dimensional HSIs are reduced to low-dimensional images. Through drop-down boxes, users can freely specify images that participate in the combination of RGB channels of the output image. Users can then interactively and independently set the fusion coefficient of each image within an interface based on concentric circles. At the same time, the output image will be calculated and visualized in real time, and the information it reflects will also be different. In this approach, channel combination and fusion coefficient setting are two independent processes, which allows users to interact more flexibly according to their needs. Furthermore, this approach is also applicable for interactive visualization of other types of multi-layer data.

scholarly journals LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4112 ◽  
Author(s):  
Se-Min Lim ◽  
Hyeong-Cheol Oh ◽  
Jaein Kim ◽  
Juwon Lee ◽  
Jooyoung Park
Keyword(s):  
Time Series ◽  
State Space ◽  
Time Series Data ◽  
State Space Model ◽  
Skill Assessment ◽  
Series Data ◽  
High Dimensional ◽  
Table Tennis ◽  
Space Model ◽  
Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

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